Abstract : The broad term goal of this research program was to build a foundation for constructing probabilistic-dynamic systems from principles based on quantum as opposed to classical probability theory. So far we have applied these principles to both traditional, one-stage decision problems studied by decision researchers as well as dynamic Markov decision problems used in computer science and engineering. The more specific goal of the proposed research was to develop new applications of quantum probability applied to dynamic decision situations: (a) To develop a quantum reinforcement learning model for learning a sequence of actions in a Markov decision problem environments that is fast learning and robust with respect to changes in the environment; (b) To theoretically derive the convergence and speed of convergence properties of the new quantum learning algorithm for the dynamic environments; and most importantly, (c) To experimentally test whether the quantum reinforcement learning model provides a better account of actual human performance in Markov de
Abstract : The broad term goal of this research program was to build a foundation for constructing probabilistic-dynamic systems from principles based on quantum as opposed to classical probability theory. So far we have applied these principles to both traditional, one-stage decision problems studied by decision researchers as well as dynamic Markov decision problems used in computer science and engineering. The more specific goal of the proposed research was to develop new applications of quantum probability applied to dynamic decision situations: (a) To develop a quantum reinforcement learning model for learning a sequence of actions in a Markov decision problem environments that is fast learning and robust with respect to changes in the environment; (b) To theoretically derive the convergence and speed of convergence properties of the new quantum learning algorithm for the dynamic environments; and most importantly, (c) To experimentally test whether the quantum reinforcement learning model provides a better account of actual human performance in Markov de
Quantum probability theory provides a new formalism for constructing probabilistic and dynamic systems of cognition and decision. The purpose of this chapter is to introduce psychologists to this fascinating theory. This chapter is organized into six sections. First, some of the basic psychological principles supporting a quantum approach to cognition and decision are summarized; second, some notations and definitions needed to understand quantum probability theory are presented; third, a comparison of quantum and classical probability theories is presented; fourth, quantum probability theory is used to account for some paradoxical findings in the field of human probability judgments; fifth, a comparison of quantum and Markov dynamic theories is presented; and finally, a quantum dynamic model is used to account for some puzzling findings of decision-making research. The chapter concludes with a summary of advantages and disadvantages of a quantum probability theoretical framework for modeling cognition and decision.
The current natural evolution of the world of real-time decision-making algorithms is unable to keep up with the fast changing complexity and dynamics of today’s world. Particularly in automotive, smart grids, robotics, or other applying fields, such ultra efficient decision making is demanded in a situation of rapidly changing conditions with high requirements on computation resources. As the first contribution, Quantum Inspired Reinforcement Learning (QIRLF) proposes a new method of addressing these challenges via marrying the fundamental elements of quantum theory to reinforcement learning. At the same time, QIRLF exploits quantum inspired state representation to explore many potential states concomitantly, thereby improving the efficiency in its decisions making process. Besides quantum tunneling and probabilistic action choice mechanisms faster convergence to optimal solutions are possible in values of state spaces, and multi-agent entanglement improves cooperation between the agents. The framework is adaptable in being able to make real time decisions in dynamic environments and is efficient by having quantum feedback loops that continuously refine decision policies. QIRLF reduces significantly the decision-making time and computational load compared to traditional, by using quantum inspired techniques. By applying this approach we not only enhance decision speed and reliability but also help in developing effective, energy efficient solutions for the complex real time systems, making it possible for more advanced, environment friendly technologies in systems needing fast, accurate and quick decisions.
Combining quantum computing techniques in the form of amplitude amplification with classical reinforcement learning has led to the so-called “hybrid agent for quantum-accessible reinforcement learning”, which achieves a quadratic speedup in sample complexity for certain learning problems. So far, this hybrid agent has only been applied to stationary learning problems, that is, learning problems without any time dependency within components of the Markov decision process. In this work, we investigate the applicability of the hybrid agent to dynamic RL environments and thus to more realistic scenarios. To this end, we enhance the hybrid agent by introducing a dissipation mechanism and, with the resulting learning agent, perform an empirical comparison with a classical RL agent in an RL environment with a time-dependent reward function. Our findings suggest that the modified hybrid agent can adapt its behavior to changes in the environment quickly, leading to a higher average success probability compared to its classical counterpart.
The increasing complexity of modern decision-making environments has challenged the effectiveness of classical mathematical models. Traditional probabilistic frameworks often struggle to represent uncertainty, ambiguity, contextual dependence, and nonlinear interactions among decision variables. Quantum-inspired mathematical models have emerged as a promising interdisciplinary approach that leverages mathematical principles derived from quantum theory without requiring quantum computing hardware. These models utilize concepts such as superposition, interference, entanglement, and contextuality to represent complex decision processes more accurately. This paper explores the theoretical foundations, mathematical structures, and applications of quantum-inspired decision models in complex systems. The study examines how quantum probability theory provides a more flexible representation of human cognition, organizational decision-making, financial forecasting, and artificial intelligence systems. Furthermore, the paper discusses mathematical formulations, implementation strategies, advantages, challenges, and future research directions. The findings suggest that quantum-inspired models offer significant potential for addressing uncertainty and dynamic interactions in complex decision environments, thereby contributing to the advancement of intelligent decision support systems.
This paper introduces a quantum framework for addressing reinforcement learning (RL) tasks, grounded in the quantum principles and leveraging a fully quantum model of the classical Markov decision process. By employing quantum concepts and a quantum search algorithm, this work presents the implementation and optimization of the agent-environment interactions entirely within the quantum domain, eliminating reliance on classical computations. Key contributions include the quantum-based state transitions, return calculation, and trajectory search mechanism that utilize quantum principles to demonstrate the realization of RL processes through quantum phenomena. The implementation emphasizes the fundamental role of quantum superposition in enhancing computational efficiency for RL tasks. Results demonstrate the capacity of a quantum model to achieve quantum enhancement in RL, highlighting the potential of fully quantum implementations in decision-making tasks. This work not only underscores the applicability of quantum computing in machine learning but also contributes to the field of quantum reinforcement learning by offering a robust framework for understanding and exploiting quantum computing in RL systems.
Abstract Markov decision process (MDP) offers a general framework for modelling sequential decision making where outcomes are random. In particular, it serves as a mathematical framework for reinforcement learning. This paper introduces an extension of MDP, namely quantum MDP (qMDP), that can serve as a mathematical model of decision making about quantum systems. We develop dynamic programming algorithms for policy evaluation and finding optimal policies for qMDPs in the case of finite-horizon. The results obtained in this paper provide some useful mathematical tools for reinforcement learning techniques applied to the quantum world.